On the wall of Roger Berkowitz’s office hangs a framed letter from Julia Child, written the day before she died.

Mr. Berkowitz is president and chief executive of Legal Sea Foods, the Boston-based seafood counter and 33-location restaurant group his parents started in 1950. He remembers Ms. Child as a loyal customer and family friend.

“We were her fish store,” says Mr. Berkowitz, who has teenage memories of Ms. Child, a tall...